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The X control chart for monitoring process shifts in mean and variance

机译:X控制图,用于监控过程均值和方差的变化

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摘要

Control charts are widely used in statistical process control (SPC) to monitor the quality of products or production processes. When dealing with a variable (e.g., the diameter of a shaft, the hardness of a component surface), it is necessary to monitor both its mean and variability (Montgomery 2009 [Montgomery, D.C., 2009. Introduction to statistical quality control. New York: John Wiley & Sons.]). This article studies and compares the overall performances of the X chart and the 3-CUSUM chart for this purpose. The latter is a combined scheme incorporating three individual CUSUM charts and is considered as the most effective scheme for detecting mean shift δ_μ and/or standard deviation shift δ_σ in current SPC literature. The results of the performance studies reveal two interesting findings: (1) the best sample size n for an X chart is always n= 1, in other words, the simplest X chart (i.e., the X chart with n= 1) is the most effective X chart for detecting δ_μ and/or δ_σ; (2) the simplest X chart often outperforms the 3-CUSUM chart from an overall viewpoint unless the latter is redesigned by a difficult optimisation procedure. However, even the optimal 3-CUSUM chart is only slightly more effective than the X chart unless the process shift domain is quite small. Since the X chart is very simple to understand, implement and design, it may be more suitable in many SPC applications, in which both the mean and variance of a variable need to be monitored.
机译:控制图广泛用于统计过程控制(SPC)中,以监视产品或生产过程的质量。在处理变量(例如,轴的直径,组件表面的硬度)时,有必要监视其均值和变异性(Montgomery 2009 [Montgomery,DC,2009.统计质量控制简介。纽约:John Wiley&Sons。])。本文研究并比较了X图表和3-CUSUM图表的总体性能。后者是结合了三个单独的CUSUM图的组合方案,被认为是检测当前SPC文献中的平均偏移δ_μ和/或标准偏差偏移δ_σ的最有效方案。性能研究的结果揭示了两个有趣的发现:(1)X图表的最佳样本大小n始终为n = 1,换句话说,最简单的X图表(即n = 1的X图表)为用于检测δ_μ和/或δ_σ的最有效X图表; (2)从总体上看,最简单的X图表通常胜过3-CUSUM图表,除非通过困难的优化程序对其进行了重新设计。但是,除非过程转换域非常小,否则即使是最佳3-CUSUM图也仅比X图稍微有效。由于X图表非常易于理解,实现和设计,因此它可能更适合于许多SPC应用程序,在这些应用程序中,变量的均值和方差都需要监视。

著录项

  • 来源
    《International Journal of Production Research》 |2012年第4期|p.893-907|共15页
  • 作者单位

    School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;

    School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;

    School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore;

    School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    quality control; statistical process control; shewhart chart; CUSUM chart;

    机译:质量控制;统计过程控制;休瓦特图;CUSUM图;

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